We aim to apply principles of combinatorial topology and statistical mechanics to the prediction of protein stability. The goal is to enumerate the chain configurations in the globular states of protein molecules subject to known energetic or distance constraints. We plan to predict entropies of folding, the accessiblities of various chain conformations, and their approximate free energies principally through exhaustive simulation of the "Hamiltonian paths" of chain molecules on lattices, weighted with appropriate interaction energies, and through use of Delaunay graphs, which are "duals" of Voronoi lattices, and related methods. Previous approaches, including molecular mechanics, molecular dynamics, and lattice treatments, have only permitted sampling of relatively small fractions of conformational space, and thus cannot predict entropies and true free energies. It appears that exhaustive simulations have not been previously attempted due to the widely held misconception that the number of chain conformations available to globular proteins is virtually infinite. We have recently shown that the number of accessible conformations has been overestimated by many tens of orders of magnitude, and is small enough to be computer enumerable. If the proposed work is successful, it should have major impact on the protein folding problem inasmuch as it bears directly on the role of chain conformations and conformational entropy in the packing and stability of globular molecules.